3.23 Mathematics (statistics)

Procedures for statistics.

3.23.1 statistical data

Function: statistics-data real …

creates a statistical data from the given numbers.

Function: histogram real …

creates a histogram from the given numbers.

Function: make-statistics-xy-data (x …) (y …)

creates an XY data from the given numbers.

3.23.2 Distribution functions

Function: make-normal-distribution mu sigma

creates a normal distribution function whose mean is \mu and variance is \sigma^2.
The result can use as a function which has one argument.

Function: make-binormal-distribution n p

creates a binomial distribution function whose number of trials is i and success probability in each trial is p(0<p<1).

Function: make-chi-squared-distribution k

creates a chi-squared distribution whose degrees of freedom is k.

Function: make-continuous-uniform-distribution a b

creates a continuous uniform distribution whose range is [a, b].

Function: make-discrete-uniform-distribution a b

creates a discrete uniform distribution whose range is [a, b].

Function: make-erlang-distribution k lambda

creates a Erlang distribution whose shape is k and rate is \lambda.

Function: make-exponential-distribution lambda

creates a exponential distribution whose rate is \lambda.

Function: make-gamma-distribution k theta

creates a gamma distribution whose shape is k and rate is \theta.

Function: make-poisson-distribution lambda

creates a Poisson distribution whose parameter is \lambda.

Function: make-t-distribution nu

creates a Student’s t-distribution whose degrees of freedom is \nu.

Function: distribution-expected-value distribution

Function: distribution-median distribution

Function: distribution-mode distribution

Function: distribution-variance distribution

Function: distribution-skewness distribution

Function: distribution-kurtosis distribution

computes expected value, median, mode, variance, skewness and kurtosis, respectively.
The argument must be a distribution function or data which is created by statistics-data.

Function: distribution-p-eq distribution a

Function: distribution-p-lt distribution a

Function: distribution-p-gt distribution a

computes probability of a distribution function where P(x=a), P(x<a) and P(x>a) respectively.

Function: pdf-to-list distribution distribution min max dx

Function: cdf-to-list distribution distribution min max dx

gets a list of values of probability density function (cumulative distribution function) in [min, max].

3.23.3 Statistical hypothesis testing

Function: test-fit-chi-squared? (observed …) (expeceted …) critical-value

tests the arguments by chi-squared test.
This procedure returns #f if the null hypothesis is rejected.

Function: test-t-1sample (observed …) expected side critical-value

tests the arguments by one-sample Student’s t-test.
Arguemt side must be a symbol shown as follows.

<	lower
>	upper
=	both

This procedure returns #f if the null hypothesis is rejected.

Function: test-t-1sample (observed …) (observed2 …) side critical-value

tests the arguments by two-sample Student’s t-test.
This procedure returns #f if the null hypothesis is rejected.

3.23.4 XY data

Function: covariance xy-data

Function: covariance (x …)(y …)

computes covariance of the given data.

Function: correlation-coefficient xy-data

Function: correlation-coefficient (x …)(y …)

computes correlation coefficient of the given data.

Function: linear-regression xy-data

Function: linear-regression (x …)(y …)

computes a polynomial by linear regression.

Function: error-term xy-data

Function: error-term (x …)(y …)

computes error term of the XY data as a statistical data.

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